Generating function
$$U_{1068}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right)^{3} \left(1 - \sqrt{1 - 4 y}\right)}{16 x^{3} y}$$
Explicit formula
$$T_{1068}(n, m, k) = \frac{3 k^{2} {\binom{k + 2 m - 1}{m}} {\binom{3 k + 2 n - 1}{n}}}{\left(k + m\right) \left(3 k + n\right)}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
3 | 3 | 6 | 15 | 42 | 126 | 396 |
9 | 9 | 18 | 45 | 126 | 378 | 1188 |
28 | 28 | 56 | 14 | 392 | 1176 | 3696 |
9 | 9 | 18 | 45 | 126 | 378 | 1188 |
297 | 297 | 594 | 1485 | 4158 | 12474 | 39204 |
1001 | 1001 | 2002 | 5005 | 14014 | 42042 | 132132 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #1068?